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arXiv:1107.2501 · Physical Review A

Multichannel effects near confinement-induced resonances in harmonic waveguides

Vladimir S. Melezhik, Peter Schmelcher

Published Oct 18, 2011• 26 citations
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Abstract

We analyze the impact of multichannel scattering in harmonic waveguides on the positions and widths of confinement-induced resonances for both isotropic and anisotropic transversal confinement. Multichannel scattering amplitudes and transmission coefficients are calculated and used to characterize the resonant behavior of atomic collisions with varying anisotropy. A mechanism is established which leads to a splitting of the confinement-induced resonance in the presence of anisotropy.

DOI
10.1103/physreva.84.042712

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We analyze the impact of multichannel scattering in harmonic waveguides on the positions and widths of confinement-induced resonances for both isotropic and anisotropic transversal confinement. Multichannel scattering amplitudes and transmission coefficients are calculated and used to characterize the resonant behavior of atomic collisions with varying anisotropy. A mechanism is established which leads to a splitting of the confinement-induced resonance in the presence of anisotropy.
We have developed the general grid method for multichannel scattering of bosonic atoms inside a harmonic waveguide with transverse anisotropy. This approach is employed to analyze elastic as well as inelastic multichannel confined scattering. For the elastic scattering, the effects of the range and form of interatomic potential and the waveguide anisotropy on the confinement-induced resonance are studied. We have also investigated quantitatively the reactive rate constant in confined atom-atom collisions. It is found that a slight anisotropy to the confining trap considerably enhances the reactive rate constant in multichannel regime.
We develop a grid method for multichannel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency $\ensuremath{\omega}$ permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic, and heteronuclear collisions. In the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.
We perform an analytical investigation in the framework of generalized KKK-matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular, we present the unitarity bounds which emerge when considering a quasi-one-dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de)excitations by means of CIRs. We analyze the CIR for ddd waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.
We develop and analyze a theoretical model which yields the shifts and widths of Feshbach resonances in an atomic waveguide. It is based on a multichannel approach for confinement-induced resonances (CIRs) and atomic transitions in the waveguides in the multimode regime. In this scheme we replace the single-channel scalar interatomic interaction by the four-channel tensorial potential modeling resonances of broad, narrow, and overlapping character according to the two-channel parametrization of Lange et al. [Phys. Rev. A 79, 013622 (2009)]. As an input the experimentally known parameters of Feshbach resonances in the absence of the waveguide are used. We calculate the shifts and widths of sss-, ddd-, and ggg-wave magnetic Feshbach resonances of Cs atoms emerging in harmonic waveguides as CIRs and resonant enhancement of the transmission at zeros of the free space scattering length. We have found the linear dependence of the width of the resonance on the longitudinal atomic momentum and quadratic dependence on the waveguide width. Our model opens possibilities for quantitative studies of the scattering processes in ultracold atomic gases in waveguides beyond the framework of sss-wave resonant scattering.
We develop the theory of anharmonic confinement-induced resonances (ACIRs). These are caused by anharmonic excitation of the transverse motion of the center of mass (c.m.) of two bound atoms in a waveguide. As the transverse confinement becomes anisotropic, we find that the c.m. resonant solutions split for a quasi-one-dimensional (1D) system, in agreement with recent experiments. This is not found in harmonic confinement theories. A new resonance appears for repulsive couplings (a3D>0{a}_{\text{3D}}>0a3D​>0) for a quasi-two-dimensional (2D) system, which is also not seen with harmonic confinement. After inclusion of anharmonic energy corrections within perturbation theory, we find that these ACIRs agree extremely well with anomalous 1D and 2D confinement-induced resonance positions observed in recent experiments. Multiple even- and odd-order transverse ACIRs are identified in experimental data, including up to N=4N=4N=4 transverse c.m. quantum numbers.
We theoretically investigate the confinement-induced resonance for quasi-one-dimensional quantum systems under transversely anisotropic confinement, using a two-body sss-wave-scattering model in the zero-energy collision limit. We predict a single resonance for any transverse anisotropy, whose position shows a slight downshift with increasing anisotropy. We compare our prediction with the recent experimental result by Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)], in which two resonances are observed in the presence of transverse anisotropy. The discrepancy between theory and experiment remains to be resolved.